How about "moff animal world" ?
You see some protection dogs there and you can touch & hug them.
If you keep a dog, you can also feed dogmeal there, too.
There are many, many dog cafe in Tokyo where you can enjoy cafe with your dog. There is one in Sky tree called Dog dept cafe. http://www.tokyo-solamachi.jp/shop/16/
If you meant a Dog cafe that you can play with the doggies, then how about わんにゃん (wan nan) Cafe & Pet Hotel Neo Neo? The Cat Cafe is located on the 1st floor, and the Dog Cafe is located on the 2nd floor.